Title: On selection dynamics for a nonlocal phenotype-structured model Show Chinese title

Title: 关于非局部表型结构模型的选择动力学

Abstract: This paper is devoted to the analysis of the long-time behavior of a phenotypic-structured model where phenotypic changes do not occur. We give a mathematical description of the process in which the best adapted trait is selected in a given environment created by the total population. It is exhibited that the long-time limit of the unique solution to the nonlocal equation is given by a Dirac mass centered at the peak of the fitness within or at the boundary of the region where the initial data is positive. Specially, If the peak of the fitness can't be in the support of the solution, then the infinite time blow-up of the solution occurs near the boundary of the region where the solution is positive. Moreover, our numerical results facilitate a deeper understanding of identifying the position of the centers. Show Chinese abstract

Abstract: 本文致力于分析一个表型结构模型的长时间行为，其中表型变化不会发生。 我们给出了在给定环境中，适应性最佳的特征被选择的过程的数学描述。 结果表明，非局部方程的唯一解在长时间极限下的结果是由集中在初始数据正值区域内的适应度峰值处或边界上的狄拉克δ函数给出的。 特别地，如果适应度峰值不能位于解的支持集内，则解会在解正值区域的边界附近出现无限时间发散。 此外，我们的数值结果有助于更深入地理解识别中心位置的过程。